论文标题
平面边界和抛物线子组
Planar boundaries and parabolic subgroups
论文作者
论文摘要
我们研究了相对双曲线对的Bowditch边界，重点是没有切割点的情况。我们表明，如果$（g，\ nathcal {p}）$是一个刚性相对双曲的组对，其边界嵌入$ s^2 $，则边界上的操作扩展到$ s^2 $的收敛组动作。更一般而言，如果连接边界并没有切割点的平面，我们表明$ \ Mathcal {p} $的每个元素实际上都是表面组。这个结论与这样的$ g $几乎是克莱恩人的猜想是一致的。我们举了许多例子来表明我们的假设的必要性。
We study the Bowditch boundaries of relatively hyperbolic group pairs, focusing on the case where there are no cut points. We show that if $(G,\mathcal{P})$ is a rigid relatively hyperbolic group pair whose boundary embeds in $S^2$, then the action on the boundary extends to a convergence group action on $S^2$. More generally, if the boundary is connected and planar with no cut points, we show that every element of $\mathcal{P}$ is virtually a surface group. This conclusion is consistent with the conjecture that such a group $G$ is virtually Kleinian. We give numerous examples to show the necessity of our assumptions.
